ar X iv : 0 90 1 . 08 58 v 2 [ cs . D M ] 1 3 A ug 2 00 9 Weighted Well - Covered Graphs without Cycles of Length 4 , 6 and 7
نویسندگان
چکیده
A graph is well-covered if every maximal independent set has the same cardinality. The recognition problem of well-covered graphs is known to be co-NP-complete. Let w be a weight function defined on the vertices of G. Then G is w-well-covered if all maximal independent sets of G are of the same weight. The set of weight functions w for which a graph is w-well-covered is a vector space. We prove that finding the vector space of weight functions under which an input graph is w-well-covered can be done in polynomial time, if the input graph does not contain cycles of length 4, 6 and 7.
منابع مشابه
ar X iv : 0 90 8 . 01 53 v 1 [ m at h . G T ] 2 A ug 2 00 9 On Fibonacci knots
We show that the Conway polynomials of Fibonacci links are Fibonacci polynomials modulo 2. We deduce that, when n 6≡ 0 (mod 4) and (n, j) 6= (3, 3), the Fibonacci knot F (n) j is not a Lissajous knot. keywords: Fibonacci polynomials, Fibonacci knots, continued fractions
متن کاملar X iv : 0 80 8 . 01 63 v 1 [ cs . D S ] 1 A ug 2 00 8 Twice - Ramanujan Sparsifiers ∗
We prove that for every d > 1 and every undirected, weighted graph G = (V, E), there exists a weighted graph H with at most ⌈d |V |⌉ edges such that for every x ∈ IR , 1 ≤ x T LHx x LGx ≤ d + 1 + 2 √ d d + 1 − 2 √ d , where LG and LH are the Laplacian matrices of G and H , respectively.
متن کاملar X iv : c s / 06 08 12 3 v 1 [ cs . I T ] 3 1 A ug 2 00 6 Proof of a Conjecture of Helleseth Regarding Pairs of Binary m - Sequences ∗
–Binary m-sequences are maximal length sequences generated by shift registers of length m, that are employed in navigation, radar, and spread-spectrum communication. It is well known that given a pair of distinct m-sequences, the crosscorrelation function must take on at least three values. This correspondence shows the three correlation values are symmetric about -1. The main result is a proof...
متن کامل